Robust pole location for a DC-DC converter through parameter dependent control

This paper addresses the problem of robust control design for a DC-DC buck converter by means of a parameter dependent state feedback gain. Sufficient conditions are given for the existence of a robust stabilizing control law which assures that, for the uncertain closed-loop system, a prespecified pole location exists inside a circle on the left-hand half of the complex plane. The output load is considered as an uncertain parameter belonging to a known interval (polytope type uncertainty). The control gain changes as the load varies, allowing us to impose to the closed-loop system a dynamic behavior that cannot be achieved through a fixed gain. The robust stabilizability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the uncertainty polytope. Simulation results illustrate the proposed method.